228
Ind. Eng. Chem. Res. 1987, 26, 228-236
Desrosiers, R. In A Survey of Biomass Gasification;Reed, T . B., Ed.; National Technical Information Service: Washington, DC, 1979; Vol. 11, SERI/TR-33-239. Groeneveld, M. J.; Van Swaaij, W. P. M. ACS Symp. Ser. 1980,33, 130.
Kunii, D.; Levenspiel, 0. Fluidization Engineering; Wiley: New York, 1969; pp 61-69. Tabatabaie-Raissi, A. PbD. Dissertation, University of California at Berkeley, Berkeley, CA, 1982. Yoon, H.; Wei, J.; Denn, M. M. AZChE J . 1978, 24, 885.
Holman, J. P. Heat Transfer, 4th ed.; McGraw-Hill: New York, 1976. Kosky, P. G.; Floess, J. K. Ind. Eng. Chem. Process Des. Deu. 1980, 19. ,586.
Receiued for review October 10, 1983 Revised manuscript receiued June 11, 1986 Accepted July 17, 1986
Mass-Transfer Characteristics of Valve Trays Richard D. Scheffe and Ralph H. Weiland* Department of Chemical Engineering, Clarkson Uniuersity, Potsdam, New York 13676
Gas- and liquid-side mass-transfer coefficients and gas-liquid interfacial areas for Glitsch V-1 valve trays are reported. T h e data were taken from a three-tray column, each tray having an active deck area of 0.372 m 2 at a tray spacing of 0.61 m. Gas and liquid rates covered the range from severe weeping to loading conditions, and weir heights were varied from 22 to 150 mm. T h e results are presented in terms of Sherwood numbers for mass transfer as functions of gas and liquid Reynolds numbers, dimensionless weir height, and Schmidt numbers. In the design of tray columns for separation processes, the usual procedure is to determine the number of equilibrium stages required and then to apply a correction for stage efficiency. To compute these stage efficiencies, one needs information on the number of transfer units for the gas and liquid phases or, equivalently, the gas and liquid side mass-transfer coefficients. For processes involving liquid-phase chemical reactions, on the other hand, the equilibrium stage model corrected for efficiencies is not a workable approach at all. This is because of the difficulty in computing the highly composition-dependent tray efficiencies in the first place, as well as the fact that efficiencies can vary quite markedly from tray to tray and component to component. In such cases, column design and simulation is more sensibly approached from the standpoint of a mass-transfer rate process. Liquid-side transfer coefficients are corrected for chemical reaction effects through the use of enhancement factors, and the whole efficiency question is circumvented altogether. This formulation often requires interfacial areas to be known separately from the individual-phase mass-transfer coefficients. Although a fair amount of mass-transfer data are available for various packings (Au-Yeungand Ponter, 1983; Bravo and Fair, 1982; Linek et al., 1984), similar information for various types of trays is quite sparse. The literature up to 1966 has been nicely summarized by K&tAnek and Standart (1966). Information on bubble-cap trays is the most complete (AIChE Bubble Tray Design Manual, 1958), and further data appearing since 1966 include those of Sharma et al. (1969), McLachlan and Danckwerts (1972), Burgess and Calderbank (1969) and Kochetov and Rodionov (1977). These latter works, however, added little to the available data base. Mass-transfer-coefficient data for sieve trays (Calderbank, 1959; Calderbank and Moo-Young, 1961; Harris and Roper, 1963; Sharma and Gupta, 1967; Pasiak-Bronikowska, 1969; Pohorecki, 1968; Counce and Perona, 1979) tends to be much more scanty due to the wide variation in tray designs, the fact that sieve trays can be operated both with and without downcomers, and the use in some cases of a tray with a single sieve hole. To our knowledge, there are no mass-transfer data based on gas absorption
processes available in the open literature for the more modern valve or ballast tray; there are, however, voluminous tray efficiency data based on distillation experiments which is some instances can be used to calculate gas-side mass-transfer coefficients. Here we report gas- and liquid-side mass-transfer coefficients and effective interfacial areas for V-1 type valve trays manufactured by Glitsch, Inc. The data were taken on a three-tray column, each tray having an active deck area of 0.372 m2 at a tray spacing of 0.61 m. The central tray was the test tray, and measurements were made by using the now-standard procedures of chemically reactive absorption. Flow conditions through the column were varied from severe weeping to entrainment conditions, and weir heights were varied from 22 to 155 mm. The results are presented in terms of Sherwood numbers (dimensionless mass-transfer Coefficients) and interfacial areas as functions of gas and liquid Reynolds numbers, dimensionless weir height, and Schmidt numbers, and so they should be able to be used for any system of known physical and transport properties.
Experimental Section Equipment. Schematic diagrams showing the experimental setup and the principal dimensions of the column are shown in Figures 1 and 2, respectively. The column was of rectangular cross section and was constructed of 19-mm cast acrylic sheet bolted together and sealed with silicone caulk. The trays were Glitsch V-1 ballast type made of 14-gauge 304 stainless steeL The trays were square, each with a bubbling area of 0.372 m2 on a spacing of 610 mm. Each tray contained 50 standard (1 7/s-in. diameter) Glitsch V-1 ballast units. The column internals were designed with provision for adjustable weir heights from 22 to 155 mm and adjustable downcomer seals. To prevent entrained liquid from leaving the column in the gas stream, a 150-mm thick by 560-mm square demister (Otto York, Inc.) was placed 200 mm above the deck of the top tray. Access to each tray was had through 300-mm by 650-mm doors. The setup permitted liquid circulation rates from about 1.1to 6.9 kg/s (8700-55000 lb/h) and air rates in the range 0.11-1.1 kg/s (200-2000 scfm). All flow rates were mea-
088S-S88S/87/2626-0228~01.~0/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 229 CYLINDER BANK
ROTAMETER
HEATEXCHAYOER
u
A I R IN
O R I F I C E METER
I
r
FLOW CONTROL
I
A I R OUT
..
BLOWER
ORIFICE METER
CALIBRATION L I N E VALVE-TRAY
" \I
COLUMN
LIQUID SAMPLER
moTTou8 PUMP TRAY OURFACE 1
akGAS
I I
SAMPLER
MIST KNOCKOUT CONE
i
ml-l
Figure 3. Gas and liquid sampling devices.
Figure 1. Schematic diagram of apparatus. GAS EXIT
DEMISTER
GAS SAMPLE PORTS
I I
75'
QAS ENTRANCE L U l D EXIT
I
tc--'--I Figure 2. Schematic diagram of valve-tray column.
sured with standard orifice plates having D and D l 2 taps. The solute gases (SOzand COJ passed through a rotameter and entered the air flow upstream of the blower, ensuring a well-mixed gas phase prior to entry into the column. The central tray was the test tray. Gas samples were taken above and below this tray through a baffled conical sampler to remove entrained droplets. Liquid samples were taken from the base of the upstream downcomer and from the flow over the exit weir through a baffled skimming device. These sample devices are shown in Figure 3, and further details are given by Scheffe (1984). All experiments performed required measurement of absorption rates. In most cases these rates were determined by gas-side analysis using gas chromatography. To ascertain the reliability of gas sampling and analysis, experiments were performed to attempt to close a mass balance about the test tray. The results of these experiments indicated that gas-side sampling and analysis were accurate-mass balances about both phases were closed to within &5%, with error equally distributed about zero (complete details are in Scheffe (1984)). Procedure for kGa Determination. Gas-side masstransfer coefficients were calculated from measured absorption rates of SO2 from air into caustic soda solutions of approximately unit normality. The gas phase was usually about 0.1 mol % SO2, and absorption rates were based on the gas flow rate and the change in gas-phase SOz concentration. Gas analysis was by gas chromatography using a 760-mm-long by 3-mm-diameter Teflon column packed with 80-100-mesh Poropak Super Q (stainless steel is unsuitable for measuring SOz). Liquid analysis was by iodimetric titration (Vogel, 1951) for sodium sulfite. During all experiments, 0.5% by volume glycerol was added to the liquid to inhibit air oxidation of sulfite to sulfate (Sharma and Gupta, 1967). The reaction between SO2 and NaOH SOz + 2NaOH = Na2S03 + HzO (1)
230 Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987
is instantaneous and irreversible. It is typical of a reaction of the type A zB = y P (2)
mass-transfer rate can be written in terms of the gas-side mass-transfer coefficient N = kGa(p - p i ) = k G a ( H p- A * ) (10)
for which the enhancement factor is
This can be solved for A* with the result that A* = ( p - N / k c a ) H
+
E = 1 + DBB0/zDAAo
(3)
It is convenient to choose conditions such that the gasphase partial pressure of the transferring species a t the interface is zero. This eliminates the need for liquid-phase concentration measurements, and it ensures that masstransfer rates are controlled entirely by diffusion in the gas phase. The criterion for purely gas-phase control is (Danckwerts, 1970, p 149)
kGap < kLoaDBBo/zDA
(4)
in which case the absorption rate is
N = kGap
(5)
where p is the bulk gas-phase partial pressure of the solute gas. Using values of p , Bo,DB/DA, and z of 0.0001 MPa, 1 kg-mol/m3, 0.5, and 2 (derived from typical operating conditions), respectively, we obtain
kGa/kLoa< 2500 as the numerical criterion to be satisfied. Figures 10 and 14 clearly show that this criterion was satisfied. Equation 5 gives the instantaneous absorption rate at a point, whereas rates were obtained from measurements across a tray. Assuming plug flow of the gas, the partial pressure in eq 5 should be replaced by its logarithmic mean value; this was done in the calculations. (The mass-transfer coefficients reported are based on mole fraction driving forces; accordingly, k,a and k,a are converted to kGa and kLoa by dividing by typical operating pressure (0.1 MPa) and liquid molar density (55.6 kg-mol/m3), respectively.) Determination of Interfacial Area. Interfacial area can be determined by using chemical systems that exhibit pseudo-first-order reaction kinetics. It is preferable to use a system for which the liquid-phase resistance controls the absorption process. The criterion to be met for the reaction given by eq 2 to exhibit pseudo-first-order kinetics is (Danckwerts, 1970, p 117) 3
< (DAkzBo/kL02)1/2 < (1 + D B B o / z D A A * ) / 2
(6)
under which conditions the absorption rate of solute A is given by
N = aA*(DAk2Bo)1/2
(7)
The criteria imposed by eq 6 were met during all experiments. Here it has been assumed that reaction 2 is second order and that the gas-phase resistance is negligible. Then the interfacial area can be calculated from measured absorption rates, the equilibrium physical solubility of solute gas ( A * ) ,and knowledge of the transport and kinetic parameters (DA, k,, and Bo). To ensure liquid-phase control, we must have
EHkLoa > 1). Use of a sparingly soluble gas (small H)such as C 0 2 helps to ensure that eq 6 is met; however, a fast reaction results in a large value of E so that often one must account for a gas-phase resistance. In that case, A* does not equal p / H . The
(11)
Thus, once having measured the absorption rate, N , and knowing the gas-side coefficient, k@, one can calculate the true interfacial concentration of solute gas in the liquid phase from eq 11 and use the result in eq 7 to determine the interfacial area. Interfacial areas were determined from absorption rate measurements of approximately 2 % C 0 2 in air into 1 N NaOH by using eq 7 with A* corrected for the gas-side resistance (generally less than 5 % ) . The absorption rate calculations were based on gas-phase analyses except for experiments a t weir heights of 22 and 50 mm. The relatively small volume of liquid on the trays at these small weir heights produced quite small changes in the partial pressure of C02,and changes in liquid-phase composition could be measured more accurately. Gas-side analysis was by gas chromatography using 1.8-m-long by 6-mm-diameter column packed with 80/100-mesh Poropak Q. Liquid analysis involved precipitation of carbonate with excess barium chloride followed by titration according to the standard procedures given by Vogel (1951). Use of eq 7 and 11 requires knowledge of several parameters. Diffusion coefficients of C02were calculated by using the formula of Barrett (1968) converted to SI units log
( 1 0 4 0 ~ )=
-4.1764
+ O.7125(lO3/T)
-
0.2591(103/T)z (12)
The second-order rate constant for the reaction between COz and hydroxyl ion was calculated from the correlation of Pinsent et al. (1956) at infinite dilution modified to yield the value of Nijsing et al. (1959) at 293 K and infinite dilution log k,, = 13.553 - 2895/T (13) Infinite dilution values were corrected for ionic strength according to the correlation of Nijsing et al. (1959) log (k,/k,,)
= 0.131
(14)
where I = 1 / 2 ~ c , z , c, 2 ,is the concentration (kg of ion/m3) of the ion i and 2, is its valency. The physical solubility (Henry’s) constant for COz in pure water was calculated from the expression log H , = -5.30 1140/T (15)
+
recommended by Danckwerts and Sharma (1966). Correction to H , was made for the salting out effect of various ions through the expression log H / H , = -(Ks’l’ K,”1’3 (16)
+
where KiI’ refers to NaOH and K,”I” refers to Na2C0,. Here K, = i+ + i- iG,and the following values of i, taken from Ueyama and Hatanak (1982), were used: Na+, 0.091: CO?-, 0.021; OH-, 0.066. The value for C 0 2 (-0.017) was taken from van Krevelen and Hoftijzer (1948). The gas-side mass-transfer coefficient kGa was taken from the present work for SO2 (the rationale for measuring this quantity first) and was corrected for the properties of C 0 2 by using the relation
+
k d C 0 2 ) = kcu(S0z)(DC02/DS02)1’2
(17)
Procedure for kLoaDetermination. Normally, one would prefer to measure the liquid-side coefficient, kLou, for physical absorption by using a system such as CO,
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 231 absorption into water because this gas is so sparingly soluble that liquid-phase control can be guaranteed. However, the capacity of water for COPis so low that the solution quickly approaches saturation on such an efficient device as a valve tray and absorption rates become impossibly slow to measure. Values of kLoa were determined by using the absorption of 1-470 C 0 2 from air into a sodium carbonate/bicarbonate buffer at a total ionic strength of 1.2 kg of ion/m3. The ratio C0;-/HC03- was maintained between one and two, and solutions containing 0.22 kg-mol/m3 NaHCO, and 0.44 kg-mol/m3 Na2C03 were used to achieve these conditions. The system C02-NaHC03-Na2C03 is a chemically reactive one, so care must be taken that the reaction is too slow to influence mass-transfer rates; i.e., there is insignificant reaction within the mass-transfer film. Otherwise, a physical mass-transfer coefficient will not be measured. On the other hand, it is desirable that the reaction be of sufficient rate to maintain the free C02 concentration zero in the bulk liquid phase. These constraints have been quantified by Danckwerts (p 184 ff, 1970). The condition for negligible reaction rate in the mass-transfer film is
DAkzBo
40
Y
0
PO
0 W
Cmml
Figure 9. Dependence of interfacial area on weir height a t G = 2.11 kgm-*.s-', L = 3.23 kgm%-'. Dashed line is Andrew's (1961) bubble-cap correlation, eq 28.
increase the turbulence level in the dispersion; the effect, however is relatively weak. Weir height is the most significant parameter. One might suppose that interfacial area should increase directly with liquid depth on the tray and indeed the power 516 on submergence has been suggested by Andrew (1961) for bubble cap trays: a = 325u1/2Z,5/6 (28) Here, Z, is the volume of liquid on the tray divided by the
+ 7.48W + 80.5LF - 0.533F) (29)
However, when interfacial areas for bubble-cap trays are computed from eq 28 and 29, the dashed lines on Figures 6 and 7 result. The effect of weir height on the interfacial areas for bubble-cap trays is even weaker than for valve trays, and the areas themselves are substantially lower. It should be mentioned that the bubble-cap data of Andrew (1961) and those of Sharma et al. (1969) are in substantial agreement. Their respective correlations have the same exponents on gas velocity and submergence but different multiplying constants because of the different ways in which submergence was defined in the two studies. Calderbank (1959) also reported bubble-cap tray interfacial areas, a', based on froth volume and ranging from 100 to 800 m2/m3. That study did not report froth depths; however, we can transform our reported values of a (which range from 8 to 62 m2/m2)to a range of a'values nearly identical with Calderbank's by assuming a typical froth depth of 8 cm. A later study by Calderbank and Moo Young (1961) reported a strong dependency of interfacial area on gas velocity ( U ~ G ' . ~ ) . There are two reasons why one might expect bubble caps to product less interfacial area than valve openings. In the first place, a smaller number of caps is used to service the same tray area, and since slot geometry is known to have negligible effect on tray performance (Sharma et al., 1959), a small number of caps is probably equivalent to a smaller number of valves. In the second place, bubble caps introduce the gas above the tray deck, whereas valves introduce the gas tangentially right a t the floor of the tray.
234 Ind. Eng. Chem. Res. Vol. 26, No. 2 , 1987 0.PO
0.20
0.11
0.15
n I
I
I
10
100
110
n
i
! E r,
E
.
%
Q
0 0.10
O- 0
0.10
0
3
E, Y
,,
m Y
I
m Y
> 0.06
0.01
0.00
O.tO
0
10
1 L
11
20
Figure 11. Dependence of gas-side mass-transfer coefficient on liquid rate for G = 1.89 kgm2.s-’, W = 50 mm, pG = 0.0426 kgm2.s-I, DG = 1.17 X m2.s-I. Lines are m ~ l . m - ~vG, = 1.44 X as for Figure 8.
For sieve plates, interfacial areas based on dispersion volume are in the range 2-2.5 cm2/cm3 for dispersion heights of 8-16 cm (Charpentier, 1981), i.e., 16-40 m2/m2 of tray area. In view of the wide variation in sieve plate geometry, direct comparison with sieve tray data does not seem possible. Gas-Side Mass-Transfer Coefficient, The dependence of k,a on gas and liquid rates and weir height is exemplified by the data in Figures 10-13, respectively. It can be seen that although the gas-side coefficient depends quite weakly on the liquid flow rate, it exhibits a strong dependence on both the gas rate and weir height. For bubble-cap plates, Andrew (1961) gives the following correlation for liquids having similar properties to water: k,a = 733u314z,’/3DG‘12P
+ 4.567 W - 0.238F + 87.32LF)GMS~-1/2 (31)
The dashed lines in Figures 10-12 represent eq 31 from which it can be seen that in all cases bubble trays have a gas-side transfer coefficient of about one-half the value for the valve trays. This is consistent with the differences in interfacial areas found for these two tray types. Thus, the mass-transfer coefficient, K,, itself is probably not a strong function of tray type but interfacial contact area is. When interfacial area is removed from kya, we obtain the following correlation for k,, the true mass-transfer coefficient ShGt = 45.1ReG0.50ReL4.12w!-0.13ScG0.5 (32) where She' = k,d/p&.
PO0
w Cmml Figure 12. Effect of weir height on gas-side mass-transfer coefficients for G = 2.11 kg.m%-l, L = 3.23 kg.m-2.s-’, PG = 0.041 kgm2.s-l, DG = 1.26 X m2K1. Lines as m ~ l . m - yG ~ , = 1.54 X for Figure 8. 0.25
I
0.001
I
l
l
1
I
I
I
l
l
I
I
(30)
where, again, 2, can be calculated from eq 29, and the effect of liquid flow rate and weir height are contained in the submergence, 2,. However, eq 30 is merely a recorrelation of the data collected in the AIChE study which, in terms of mass-transfer coefficients, is (Krishnamurthy and Taylor, 1985)
k,a = (0.776
0
(kg/m**sl
On the other hand, combining
0.0
1.o
l
2.0
l
3.0
1 4.0
G (kg/mZs)
Figure 13. Comparison of gas-side mass-transfer coefficient with distillation studies. Dashed’lines are as for Figure 10. FRI distillation data: (1)Glitsch A1 ballast tray with 3-in. weir, (2) Glitsch V1 ballast tray with 2-in. weir, (3) Glitsch VO ballast tray with 2.5-in. weir. Turbogrid data: (4) Huml and Standart, 1966; (5) Kastanek and Standart, 1967.
eq 28 and 30 of Andrew (1961) for bubble trays, one obtains k , = 2 . 2 5 u ’ ~ 4 z ~ 1 1 2 D ~ ’ ~ 2 p ~ (33) In particular, the effect of gas velocity on k, appears to be much weaker for bubble trays than for valve trays. The k,a values reported here can be compared with tray efficiency data taken from distillation studies. Huml and Standart (1966) explain this procedure; assuming complete liquid-phase mixing and gas-side controlled transfer, a simple expression relating k,a as a function of Murphree tray efficiency is k,a = -In (1 - 7)Gm (34)
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 235 2.0
2.0
0
1 .5
1.5 n
! E
n
! E
d
-0
0,
5
6
1.0
&
m
Y Y
Y
1.0
X
m Y
0.5
0.5
0.0
0.0
0.0 0.S
1.0 Q
1.5
2.0
2.5
3.0
Here, G, is the total vapor molar velocity (kg-mol/ (m2-s)); appropriate flow, composition, and physical property data are required to estimate G, and to transform k,a values to other systems (by eq 17 for example). By use of eq 32, comparisons of kp (reported here) with distillation studies on Glitsch valve trays (FRI, 1958; FRI, 1959; FRI, 1967) are shown in Figure 13. These data, developed for the cyclohexane-n-heptane system, are in good agreement with those reported here. Other valve tray distillation data are available (Garrett et al., 1977; Fair, 1965) but lack necessary information required to transform tray efficiency into the gas-side mass-transfer coefficient. Also shown in Figure 13 are data for Turbogrid trays (Hum1 and Standart, 1966; KaEit6nek and Standart, 1967) using the CH3OH-H,O system. (The Turbogrid data were transformed by assuming typical operating temperatures and pressures of 373 K and 0.1 MPa and 10% methanol composition.) Liquid-Side Mass-Transfer Coefficient. It can be seen from Figures 11-16 that the important parameter in determining k,a is the gas rate through the tray; the liquid rate and weir height have negligible effect. The AIChE correlation for bubble trays is (Krishnamurthy and Taylor, 1984) X
10
104(0.15+ 0.213F)tLLDL1/'
where the average liquid contact time,
tL,
20
1s
L Ckg/mm*rl
Figure 14. Liquid film coefficient as a function of gas rate for L = 3.23 kgm%-', pL = 55.5 k g - m ~ l - m -vL ~ , = 1.10 X lo4 m2.s-l, DL = 1.54 X lo4 m Z d ,and W = 22 (A),50 ( O ) , 150 mm (0). Dashed line is eq 34; dotted line is eq 36, both for bubble-cap trays.
k,= ~ 2.03
5
0
Cks/mm*rl
(35)
Figure 15. Dependence of liquid film coefficient on liquid rate a t G = 1.94 ka.m-2.s-1, W = 50 mm. Other parameters and lines as in Figure 11. a.0
1 .s n
! E
-. 1.0 Q
/
O
k
Y
m
/
X Y
/
/'
0.5
0.0 0
ZLis the average width of the liquid flow path and 2, is calculated from eq 29. Again, the dashed lines in these figures represent eq 35. The Andrew (1961) form of the AIChE correlation is
k,a = 1174u3/42,1/3DL1/2pL
so
100
W
(36)
(37)
shown by the dotted line in the figures. By and large, our data follow the same trend as eq 37 although the liquidside coefficients for bubble caps tend to be about 20% lower than for valve trays. The AIChE correlation, on the
I /
is
tL = l.POZJL/LF
I
I
1 so
200
Cmml
Figure 16. Dependence of liquid film coefficient on weir height a t G = 2.11 kgm%-', L = 3.23 kg.m%-'. Other parameters and lines as in Figure 11.
other hand, shows a much stronger dependency on weir height and a weaker dependency on gas velocity than both the Andrew correlation and our own data.
Acknowledgment This work was done under contract for The Dow Chemical Company to which we are grateful for permission to publish. R.D.S. was supported by a Dow Chemical
236 Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987
Fellowship. Thanks are expressed to Glitsch, Inc., and Gould pumps, Inc., companies which donated the valve trays and centrifugal pumps, respectively.
Nomenclature a = interfacial area per unit tray area a' = interfacial area per unit froth volume, m-' A = concentration of A, kg-m~l-m-~, or constant in eq 23 A' = constant in eq 24 B = concentration of B, kg-m~l-m-~ c i = concentration of ions of valency zit (kg of i ~ n ) . m - ~ d = characteristic length, taken as 1 m
D = diffusion coefficient, m2-s-' E = enhancement factor F = F factor, product of superficial gas velocity and square root of gas mass density, kg.m-%-' G = superficial gas mass velocity, kg.m-2.s-1 G M = superficial gas molar velocity, kg-mol-m-2.s-' H = Henry's constant, kg-m~l.m-~.MPa-' Hw = Henry's constant in water, kg-m~l.m-~.MPa-' I = ionic strength = 1/2xciZi2,(kg of i ~ n ) . m - ~ kGa = gas-side mass-transfer coefficient based on partial pressure driving force, kg-mol.m-2.s-1.MPa-' kLoa = liquid-side mass-transfer coefficient based on molar concentration difference, m-s-' k,a = liquid-side mass-transfer coefficient based on mole fraction driving force, kg-mol.m%-' k,a = gas-side mass-transfer coefficient based on mole fraction driving force, kg-mol.m-2.s-' k, = second-order reaction rate constant, m3.kg-mol-'.s-' k Z w= second-order rate constant at infinite dilution, m3.kgmo1-l.s-l K, = salting out constant, m3.(kg of ion)-' K , = equilibrium constant for dissociation of water, ((kg of 'ion).&)* K , = equilibrium value of [H+][C032-]/[HC03-],(kg of i0n)Sm-j L = superficial liquid mass velocity, kg.m%.-' LF = volumetric liquid flow rate per unit average flow path width, m2.s-' LM = superficial liquid molar velocity, kg-mol.m-2.s-' N = molar flux, kg-mol.m%-' p = partial pressure, MPa P = reaction product in eq 2 P= total pressure in eq 30, MPa ReG = gas-phase Reynolds number = Gd/FG ReL = liquid-phase Reynolds number = L d / p L Scc = Schmidt number of solute in gas = v G / & ScL = Schmidt number of solute in liquid = v L / D L Shc = gas-side Sherwood number = k,ad/p& ShL = liquid-side Sherwood number = k,ad/pLDL tL = average liquid contact time, s T = absolute temperature, K u = linear gas velocity, mss-' W = weir height, m W' = dimensionless weir height = W / d y = stoichiometric coefficient in eq 2 z = stoichiometric coefficient in eq 2 z, = valency of ionic species 2, = clear liquid depth on tray, m Z L = average liquid flow path width, m Greek Symbols = exponents in eq 23 and 24 p , p' = exponents in eq 23 and 24 y,y' = exponents in eq 23 and 24 6 = exponent in eq 23 fi = shear viscosity, kg.m-'.s-' u = kinematic viscosity, m2.s-' C YCY' ,
bulk-phase molar density, kg-m~lmm-~ = contact time, s
p = T
7 = Murphree tray efficiency
Subscripts
A = refers to solute gas B = refers to reactive component in the liquid G = referred to the gas i = at the interface L = referred to the liquid Superscripts
o = in the bulk phase
*
= at the interface
Literature Cited Andrew, S. P. S. Alta Technologia Chimica; Accadamia Nazionale dei Lincei: Roma, 1961; p 153. American Institute of Chemical Engineers Bubble-Tray Design Manual; New York, 1958. Au-Yeung, P. H.; Ponter, A. B. Can. J . Chem. Eng. 1983, 61, 481. Barrett, P. V. L. Ph.D. Thesis, University of Cambridge, Cambridge, England, 1968. Bravo, J. L.; Fair, J. R. Ind. Eng. Chem. Process Des. Deu. 1982. 22, 162. Burgess, J. M.; Calderbank, P. H. Chem. Eng. Sci. 1969, 24, 1139. Calderbank, P. H. Trans. Inst. Chem. Eng. 1959,37, 173. Calderbank, P. H.; Moo-Young, M. B. Chem. Eng. Sci. 1961,26,39. Charpentier, J. C. Aduances in Chemical Engineering; Academic: New York, 1981; pp 1-133. Counce, R. M.; Perona, J. J. Ind. Eng. Chem. Process Des. Deu. 1979, 18, 562. Danckwerts, P. V. Gas-Liquid Reactions; McGraw-Hill: New York, 1970. Danckwerts, P. V.; Sharma, M. M. Chem. Eng. J . (Lausanne) 1966 (Oct), CE 244. Fair, J. R. Chem. Eng. (N. Y.) 1965 (July 5 ) , 107. Fractionation Research, Inc. Topical Report No. 15 to Glitsch, Inc., Sept 3, 1958. Fractionation Research Inc. Topical Report No. 19 to Glitsch, Inc.. Sept 25, 1959. Fractionation Research, Inc. Topical Report No. 41 to Glitsch, Inc., Nov 10, 1967. Garrett, R. G.; Anderson, R. H.; Van Winkle, M. Ind. Eng. Chem. Process Des. Deu. 1977, 16, 79. Harris, I. J.; Roper, G. M. Can. J. Chem. Eng. 1963, 41, 158. Huml, M.; Standart, G. Br. Chem. Eng. 1966, 2 2 , 1970. KaStlnek, F.; Standart G. Efficiency of Distillation Trays; Academia, Czechoslovak Academy of Sciences: Prague, 1966; p 181. KaStknek, F.; Standart, G. Sep. Sci. 1967, 2, 439. Kochetov, N. M.; Rodinov, A. I. Zh. Prihl. Khim. (Leningrad) 1977, 50, 2624. Krishnamurthy, R.; Taylor, R. AIChE J . 1985, 31, 456. Linek, V.; Petricek, P.; Benes, P.; Braun, R. Chem. Eng. Res. Des. 1984, 62, 13. McLachlan. C. N. S.;Danckwerts, P. V. Trans. Inst. Chem. Eng. 1972, 50, 300. Nijsing, R. A.; Hendriksz, T. 0.;Kramers, H. Chem. Eng. Sci. 1959, 10, 88. Pasiak-Bronikowska, W. Chem. Eng. Sci. 1969, 24, 1139. Pinsent, B. R. W.; Pearson, L.; Roughton, F. J. W. Trans. Faraday SOC.1956, 52, 1512. Pohorecki, R. Chem. Eng. Sci. 1968,23, 1447. Roberts, D.; Danckwerts, P. V. Chem. Eng. Sci. 1962, 27, 961. Scheffe, R. D. M.S. Thesis, Clarkson University, Potsdam, NY, 1984. Sharma, M. M.; Gupta, R. K. Trans. Inst. Chem. Eng. 1967,45, 169. Sharma, M. M.; Mashelkar, R. A,; Mehta, V. D. Br. Chem. Eng. 1969, 14, 70. Ueyama, K.; Hatamak, J. Chem. Eng. Sci. 1982, 37, 790. van Krevelen, D. W.; Hoftijzer, P. J. Recl. Trau. Chim. Pays-Bas 1948, 67, 563. Vidwans, A. D.; Sharma, M. M. Chem. Eng. Sci. 1967, 22, 673. Vogel, A. I. A Testbook of Quantitatiue Inorganic Analysis; Longmans, Green and Co.: New York, 1951; p 918.
Received for review December 21, 1984 Revised manuscript received May 21, 1986 Accepted July 24, 1986
